Double Cone on Rails, 1J11.50

As a double cone moves up a set of inclined rails, its center of gravity is lowered to the height of the rails.

Equipment

Location

ID Number

Double Cone and Incline

ME, Bay , Shelf #

Important Setup Notes:

N/A

Setup and Procedure:

Place the inclined rails on a level surface.

Place the double cone at the bottom of the incline with its center between the rails.

Cautions, Warnings, or Safety Concerns:

N/A

Discussion:

This demo can be thought of like a ball on a hill: at the top of the hill, the ball is in an unstable equilibrium. An unstable equilibrium is a static situation where all of the forces acting on the object balance (their sum is zero) and hence the object has a uniform velocity. In this case, our object would have zero velocity. Unstable means that any force applied to our object will destroy the equilibrium of the ball causing it to have a net acceleration along the hill. This is certainly the case with our double cone. If you carefully place the double cone on the inclined rails, you can achieve such an unstable equilibrium; the cone will not roll up or down the rails. This should make sense if one considers the free body diagram of the system. If correctly oriented, we can achieve a perfect balance between the gravitational and normal forces acting on the double cone.

Like our ball on the hill, it has associated with it some potential energy which depends on the mass of the ball and its height above the ground. As the ball rolls down the hill, this potential energy is converted into kinetic energy. Our double cone, however, is not a point mass. As a rigid body, we can find the center of mass of our double cone which one can due by eye thanks to the symmetry of our object. When the cone is at the low end of the rail, the center of mass is above the point of contact with the rail and hence has some potential energy. The top of the rails is analogous to the bottom of our hill since this is where the center of mass is level with the point of contact with the rails.